Measuring apparatus and measuring method

ABSTRACT

A measuring apparatus is disclosed which includes an interferometer for measuring a wavefront of light transmitted through a test object by interference between light under test passed through the test object and reference light, and measures a polarization characteristic of the test object. The measuring apparatus has a measuring unit for measuring a polarization characteristic matrix in a pupil plane of the test object while the reference light is blocked or fringe scan is performed.

BACKGROUND OF THE INVENTION

The present invention generally relates to a measuring apparatus and ameasuring method, and more particularly, to a measuring apparatus and ameasuring method for measuring a polarization characteristic(birefringence) of an optical system (specifically, a projection opticalsystem) of an exposure apparatus used during a lithography process inmanufacturing various devices such as a semiconductor device and aliquid crystal display device.

In manufacturing very small devices with a photolithography technique, areduced projection exposure apparatus has been used in which aprojection optical system projects a circuit pattern onto aphotosensitive substrate such as a wafer to transfer the circuit patternto the photosensitive substrate.

The reduced projection exposure apparatus needs to transfer a reticlepattern accurately to a wafer at a predetermined scaling factor. Tosatisfy the need, it is important to use a projection optical system (aprojection lens) excellent in optical performance such as an imagingproperty. In recent years, particularly, miniaturization of devicesaccomplished at a fast pace has often required pattern transfer beyond anormal imaging property, and the pattern transfer is becoming sensitiveto birefringence which is a polarization characteristic of an opticalsystem.

Several apparatuses and methods have conventionally been proposed formeasuring birefringence. For example, a proposed apparatus measuresbirefringence by using light transmitted through a test object similarlyto a stress measuring apparatus for a semiconductor wafer. Such anapparatus, however, can only measure birefringence at a certain point ona surface of the test object (in other words, it only can perform pointmeasurement) since the apparatus has no image-forming system. Whenbirefringence needs to be measured over a wide area, scanning should beperformed for the test object (or for a light source). Thus, theapparatus is complicated and is not suitable for a test object whichneeds measurement over a wide area such as a projection optical system.To address this, another proposed apparatus enables measurement ofbirefringence of a test object over a wide area thereof by using ashearing interferometer having an image-forming system. For example,Japanese Patent Laid-Open NO. 2004-61515 has proposed such an apparatus.

The apparatus using the shearing interferometer proposed in JapanesePatent Laid-Open No. 2004-61515 measures birefringence with adiffraction grating removed, while the diffraction grating is insertedthereinto when a wavefront is measured. As a result, the apparatus isdirectly affected by birefringence in the diffraction grating, therebymaking it impossible to measure the birefringence accurately.

In addition, diffracted light emerges in a direction at an angle withrespect to the incident light, so that the direction of polarization canbe changed. It is thus difficult to eliminate the influence of theoptical system (that is, the image-forming system included in theshearing interferometer) other than the test object (such as aprojection optical system) in measuring a wavefront, and it isimpossible to provide complete consistency between the wavefrontmeasurement and the birefringence measurement. In other words, theinfluence of the optical system included in the apparatus upon thepolarization characteristic cannot be measured precisely, and thebirefringence of the test object cannot be measured accurately.

BRIEF SUMMARY OF THE INVENTION

It is an object of the present invention to provide a measuringapparatus and a measuring method which allow accurate measurement ofbirefringence of a test object over a wide area thereof.

A measuring apparatus according to one aspect of the present inventionfor measuring a polarization characteristic of a test object includes aninterferometer for measuring a wavefront of light transmitted throughthe test object by interference between light under test passed throughthe test object and reference light, and a measuring unit for measuringa polarization characteristic matrix in a pupil plane of the test objectby using fringe scan.

A measuring apparatus according to another aspect of the presentinvention includes an interferometer which measures a wavefront of lighttransmitted through a test object by interference between light undertest passed through the test object and reference light, and measuring apolarization characteristic of the test object, and a measuring unit formeasuring a polarization characteristic matrix in a pupil plane of thetest object while the optical path of the reference light is blocked.

A measuring apparatus according to yet another aspect of the presentinvention includes an interferometer which measures a wavefront of lighttransmitted through a test object by interference between light undertest passed through the test object and reference light, and measuring apolarization characteristic of the test object, and a measuring unit formeasuring a polarization characteristic matrix in a pupil plane of thetest object while the reference light is blocked by moving a spatialfilter.

A method according to another aspect of the present invention ofmeasuring a polarization characteristic of a test object by using aninterferometer which measures a wavefront of light transmitted throughthe test object by interference between light under test passed throughthe test object and reference light includes the steps of measuring apolarization characteristic matrix in a pupil plane of the test objectby using fringe scan, and calculating the polarization characteristic ofthe test object from the polarization characteristic matrix measured inthe measuring step.

A method according to yet another aspect of the present invention ofmeasuring a polarization characteristic of a test object by using aninterferometer which measures a wavefront of light transmitted throughthe test object by interference between light under test passed throughthe test object and reference light includes the steps of blocking theoptical path of the reference light, and calculating a polarizationcharacteristic matrix in a pupil plane of the test object.

A method according to a further aspect of the present invention ofmeasuring a polarization characteristic of a test object by using aninterferometer which measures a wavefront of light transmitted throughthe test object by interference between light under test passed throughthe test object and reference light includes the steps of blocking thereference light by moving a spatial filter, and calculating apolarization characteristic matrix in a pupil plane of the test object.

A measuring method according to another aspect of the present inventionincludes the steps of measuring a transmitted wavefront in the pupilplane of the test object with the abovementioned measuring apparatus,normalizing a phase term of polarization characteristic matrixdistribution in the pupil plane of the test object based on thetransmitted wavefront measured in the measuring step, and calculating atransmitted wavefront in the pupil plane of the test object for anarbitrary polarization state from the phase term of the polarizationcharacteristic matrix distribution normalized in the normalizing step.

A measuring method according to yet another aspect of the presentinvention includes the step of determining distribution of a lightamount transmitted through the test object and an optical system of theinterferometer, distribution of a light amount transmitted through theoptical system of the interferometer excluding the test object, apolarization characteristic matrix of the test object, and apolarization characteristic matrix of the optical system of theinterferometer excluding the test object by using the abovementionedmeasuring apparatus, and calculating distribution of transmittance inthe pupil plane of the test object for an arbitrary polarization statebased on the determined information.

Other objects and features of the present invention will become readilyapparent from the following description of the preferred embodimentswith reference to accompanying drawings.

According to the present invention, a measuring method and a measuringmethod can be provided which enables accurate measurement ofbirefringence of a test object over a wide area thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic section view showing the basic structure of ameasuring apparatus according to an aspect of the present invention.

FIG. 1B shows the structure of the measuring apparatus in FIG. 1 arounda stage.

FIG. 2 is a schematic section view showing the structure of themeasuring apparatus for measuring a polarization optical characteristicof a measuring optical system other than a test object.

FIG. 3 is a schematic section view showing the structure of themeasuring apparatus for measuring a polarization optical characteristicof the measuring optical system other than the test object.

FIG. 4 is a schematic section view showing the structure of a measuringapparatus according to another aspect of the present invention.

FIGS. 5(a) and 5(b) are enlarged section views showing a spatial filtershown in FIG. 4 and its surroundings.

FIGS. 6(a) and 6(b) are graphs showing the driving of a PZT actuatorshown in FIG. 4 and variations in interference patterns in a pixel of acamera.

FIG. 7 is a schematic section view showing the structure of a measuringapparatus according to another aspect of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Preferred embodiments of the present invention will hereinafter bedescribed with reference to the accompanying drawings.

Embodiment 1

FIG. 1A is a schematic section view showing the basic structure of ameasuring apparatus 1 according to an aspect of the present invention.The measuring apparatus 1 of Embodiment 1 includes a Twyman-Greeninterferometer for measuring a wavefront of light transmitted through atest object OS (a transmitted wavefront) and measures birefringence (apolarization characteristic) of the test object OS. In Embodiment 1, aprojection optical system (a projection lens) of a projection exposureapparatus is assumed as the test object OS.

Referring to FIG. 1A, luminous flux which emitted from a light source 10is transmitted through a polarizer 11 to have a predetermined (that is,a known) polarization state. The luminous flux emitting from the lightsource 10 is circularly polarized. Simply rotating the polarizer 11about the optical axis of a measuring optical system of the measuringapparatus 1 can provide a sufficient amount of arbitrarily linearlypolarized light. The measuring optical system refers to an opticalsystem having at least one optical element which directs the luminousflux from the light source 10 to the test object OS and directs thelight passing through the test object OS to a detector. For example, inEmbodiment 1, the measuring optical system consists of optical elements12, 13, 14, 21, 25, 26 and the like. The polarizer 11 is disposed to bedriven on a θ stage, not shown, and controlled by a controller, notshown. The polarizer 11 usable at the same wavelength as that of theprojection optical system (the test object OS) which is used with lightat the wavelengths of ultraviolet rays or lower includes a Rochon prismincluding magnesium fluoride (MgF₂) as a material.

The luminous flux which passed through the polarizer 11 is linearlypolarized depending on the rotation angle of the polarizer 11. Theluminous flux which passed through the polarizer 11 passes through beamexpanders 12 and 13 for increasing the beam diameter and is thenincident on a half mirror 14 as collimated luminous flux. The luminousflux reflected by the half mirror 14 and the luminous flux transmittedthrough the half mirror 14 will hereinafter be referred to as luminousflux under test and reference luminous flux, respectively.

The luminous flux under test enters an object-side XY stage 15, and asshown in FIG. 1B, is reflected by an X stage return mirror 16 to amirror 17 on a Y stage, not shown, and is then reflected by the mirror17 to an object-side Z stage 18. The return by the mirror is performedfor the purpose of providing the same optical axis with respect to thestage even when the stage is moved, so that the luminous flux may beincident on the mirrors in a different order from that in Embodiment 1.A collimator lens 19 is disposed on the object-side Z stage 18. Theobject-side Z stage 18 is driven in the optical axis direction such thatthe focal point of the collimator lens 19 is at the object surface ofthe test object OS. The object-side XY stage 15 is driven in thedirection perpendicular to the optical axis such that the focal point ofthe collimator lens 19 is at the object position where birefringence ismeasured.

The luminous flux under test which passed through the collimator lens 19and entered the test object OS passes through the test object OS and isformed into an image at an image point which is determined by themagnification of the test object OS. A spherical mirror 21 is disposedon an image-side Z stage 20. The image-side Z stage 20 and an image-sideXY stage 22 adjust the position such that the center of curvature of thespherical mirror 21 coincides with the image-forming position (the imagepoint) of the test object OS. As the spherical mirror 21, a mirror madeof raw glass or silicon (Si) crystal is used in order to avoid theinfluence of birefringence. The luminous flux under test which wasreflected by the spherical mirror 21 passes through the test object OSand is returned to the half mirror 14 along the same optical path.

On the other hand, the reference luminous flux which passed through thehalf mirror 14 is routed to travel along the optical path with the samelength as that of the luminous flux under test before reflection by areference mirror 23. The reference luminous flux which was reflected bythe reference mirror 23 is returned to the half mirror 14 along the sameoptical path and is caused to interfere with the luminous flux undertest. However, the reference luminous flux is blocked by a light shieldplate 24 when the birefringence of the test object OS is measured. Thelight shield plate 24 can be inserted into and removed from the opticalpath of the measuring optical system. The light shield plate 24 isdisposed in the optical path of the measuring optical system as shown inFIG. 1A when the birefringence is measured, while it is removed from theoptical path when the transmitted wavefront is measured.

The luminous flux under test which passed through the half mirror 14 istransmitted through pupil image-forming lenses 25 and 26 for providing aconjugate relationship between the pupil of the test object OS and acamera 29, and becomes collimated again. The collimated luminous fluxunder test is subjected to polarization modulation by a λ/4 plate 27disposed on a θ stage, not shown. Only the linearly polarized componentspecified by the angle of an analyzer 28 is transmitted through theanalyzer 28 and is taken as an image by the camera 29 serving as adetector. The θ stage, not shown, is controlled by a controller, notshown. The angle of the fast axis of the λ/4 plate 27 at the originpoint of the θstage and the angle of the transmission axis of theanalyzer 28 are adjusted in parallel with the sheet (FIG. 1A), similarlyto the transmission axis of the analyzer 28.

Embodiment 1 employs the λ/4 plate 27 as a wavelength plate forproviding a predetermined phase lag for the luminous flux under test, awavelength plate other than the λ/4 plate may be used as long as itprovides an obvious phase lag other than λ/2. A Rochon prism is used asthe analyzer 28 similarly to the polarizer 11.

Next, description will be made of a method of measuring a polarizationcharacteristic matrix of the test object OS by the measuring apparatus1. In Embodiment 1, the polarization characteristic matrix is the Jonesmatrix which represents the polarization change characteristic of apolarization element in a two-by-two (two rows and two columns) matrix.The birefringence can be derived from the Jones matrix.

First, the θ stage is driven such that the polarizer 11 is placed at anangle of θpol1. As a result, the luminous flux emerging from thepolarizer 11 is linearly polarized at the angle of θpol1. Such apolarization state is expressed as Xin1, where X represents a complexnumber given from the elements of two columns when the Jones matrix isnormalized for the elements of one column, and Xin will hereinafterreferred to as a polarization parameter.

Next, the camera 29 takes images showing the changing light amount whilethe λ/4 plate 27 is rotated. The rotation of the λ/4 plate 27 needs tobe synchronized with the taking of images of the transmitted lightamounts by the camera 29. It is possible to take images simultaneouslywith the rotation of the λ/4 plate 27 or to perform so-calledstep-and-repeat in which the rotation of the λ/4 plate 27 in steps ofsmall angles and the image taking by the camera 29 are alternated.

A polarization parameter Xout1 at the incidence on the λ/4 plate 27 iscalculated from a change in the transmitted light amount for each pixelof the camera 29 with the rotation of the λ/4 plate 27. The followingexpression 1 can be given by extracting the DC component, the secondharmonic component, and the fourth harmonic component in the transmittedlight amount change with a method such as Fourier analysis:$\begin{matrix}{\chi_{out} = \frac{{2{FHs}} - {iSHs}}{{DC} + {FHc}}} & \left( {{Expression}\quad 1} \right)\end{matrix}$where DC represents the DC component, SHs the sine component of thesecond harmonic, FHs the sine component of the fourth harmonic, and FHcthe cosine component of the fourth harmonic.

When the λ/4 plate 27 involves a phase lag error due to manufacturingerrors or the like, the phase lag may be previously measured to makecorrection in calculating the polarization with the phase shifter. Thepolarization calculation with the phase shifter is performed for all theangles of view in the pupil of the test object OS to be taken.

Such measurement is performed for the independent three incident linearpolarization states Xin1, Xin2, and Xin3 to calculate the polarizationparameters Xout1, Xout2, and Xout3.

Next, the Jones matrix J is calculated as a polarization characteristicmatrix of all the optical elements (the optical system) which transmitor reflect the luminous flux from the polarizer 11 to the λ/4 plate 27.The Jones matrix J of the optical elements normalized for elements intwo rows and two columns is calculated as the following expression 2:$\begin{matrix}{J = {\quad{{\begin{bmatrix}{\chi_{{in}\quad 2} - {\chi_{{in}\quad 1}H}} & {H - 1} \\{{\chi_{{in}\quad 2}\chi_{{out}\quad 1}} - {\chi_{{in}\quad 1}\chi_{{out}\quad 2}H}} & {{- \chi_{{out}\quad 1}} - {\chi_{{out}\quad 2}H}}\end{bmatrix}H} = \frac{\left( {\chi_{{out}\quad 3} - \chi_{{out}\quad 1}} \right)\left( {\chi_{{in}\quad 3} - \chi_{{in}\quad 2}} \right)}{\left( {\chi_{{out}\quad 3} - \chi_{{out}\quad 2}} \right)\left( {\chi_{{in}\quad 3} - \chi_{{in}\quad 1}} \right)}}}} & \left( {{Expression}\quad 2} \right)\end{matrix}$where Xin1, Xin2, and Xin3 represent the incident linear polarizationstates, and Xout1, Xout2, an Xout3 represent the polarizationparameters.

The Jones matrix J of the optical elements is also calculated for allthe angles of view in the pupil of the test object OS similarly to theemergence polarization parameters described above. The Jones matrixprovided from the structure shown in FIG. 1A is referred to as Jtest.

Next, description will be made of separation of the polarizationcharacteristic matrix of the test object OS from the polarizationcharacteristic matrix of the measuring optical system (the opticalelements) other than the test object OS. FIGS. 2 and 3 are schematicsection views showing the structure of the measuring apparatus 1 formeasuring the polarization optical characteristic of the measuringoptical system other than the test object OS.

FIG. 2 shows the structure of the measuring apparatus 1 for measuringthe polarization optical characteristic. In this case, the polarizationoptical characteristic is provided in the optical path of light whichtravels from the polarizer 11 and passes through the beam expanders 12and 13, is reflected by the half mirror 14, and is returned by areference plane mirror 30. Alternatively, it is provided in the opticalpath of light which is returned by the reference plane mirror 30 andtransmitted through the half mirror 14, the pupil image-forming lenses25 and 26. In the following, a system error 1 is defined as thestructure of the optical path of light which travels from the polarizer11 and passes though the beam expanders 12 and 13, is reflected by thehalf mirror 14, and returned by the reference plane mirror 30, and theJones matrix of the system error 1 is referred to as Jsys1.

The reference plane mirror 30 for system measurement is disposed in theoptical path of the collimated luminous flux after the transmissionthrough the beam expanders 12 and 13. Raw glass, an aluminum mirror withno protective coating or the like is used as the reference plane mirror30 to reduce the influence of the birefringence of the mirror. While thereference plane mirror 30 is disposed immediately after the half mirror14 in Embodiment 1, it may be disposed anywhere in the optical pathbefore the collimator lens 19. The Jones matrix in this state iscalculated from three emergence polarization states for three incidentpolarization states determined from rotation of the polarizer 11,similarly to the abovementioned one.

Next, a polarizer 31 is disposed in the stage after the reference planemirror 30. With the placement of the polarizer 31, the polarizationstate before the polarizer 31 is reset after the reflection by thereference plane mirror 30, so that the polarization opticalcharacteristic can be measured in the optical path of light which istransmitted through the half mirror 14 and the pupil image-forminglenses 25 and 26. In the following, a system error 2 is defined as thestructure of the optical path of light which is returned by thereference plane mirror 30 and is transmitted through the half mirror 14and the pupil image-forming lenses 25 and 26, and the Jones matrix ofthe system error 2 is referred to as Jsys2.

The polarizer 31 is installed on a θ stage, not shown, similarly to thepolarizer 11 for normal measurement, and is controlled to rotate aboutthe optical axis by a controller, not shown. The Jones matrix Jsys2 ismeasured from the results of the polarization rotation of the incidentlight by the polarizer 31. The rotation of the polarizer 11 needs to beadjusted to provide a sufficient light amount after transmission throughthe polarizer 31. The polarizer 11 may be removed to ensure a sufficientlight amount.

Referring to FIG. 3, a reference spherical mirror 32 is disposed withits center of curvature positioned at the focal point of the collimatorlens 19. In the structure, the polarization optical characteristic ismeasured in the optical path of light which is reflected by the halfmirror 14 and transmitted through the pupil image-forming lenses 25 and26. In this case, the light from the light source 10 passes through thepolarizer 11 and the beam expanders 12 and 13, is reflected by the halfmirror 14, is reflected by the return mirror 16, the mirror 17, and thecollimator lens 19 on the associated stages, and is then reflected backby those three elements along the same path, followed by incidence onthe half mirror 14. In the following, a system error 3 is defined as thestructure of the optical path of light which is reflected by the halfmirror 14, reflected by the return mirror 16, the mirror 17, and thecollimator lens 19 on the associated stages, then reflected back bythose three elements along the same path, and transmitted through thehalf mirror 14 and the pupil image-forming lenses 25 and 26. The Jonesmatrix of the system error 3 is referred to as Jsys3. The Jones matrixJsys3 is measured from the results of the polarization rotation of theincident light by the polarizer 11, similarly to the Jones matrix Jsys1.

The four Jones matrixes Jtest, Jsys1, Jsys2, and Jsys3 provided asdescribed above are used to calculate the Jones matrix of the testobject OS. Each of the respective Jones matrixes is represented as thefollowing expression 3 by using the Jones matrix of each optical element(optical system) included:Jtest=J _(HM(T)-QWP) ·J _(ColLens-HM(T)) ·J _(Lens) ·J _(Lens) ·J_(HM(R)-ColLens) ·J _(pol-HM(R))Jsys1=J _(HM(T)-QWP) ·J _(pol-HM(R))Jsys2=J _(HM(T)-QWP)Jsys3=J _(HM(T)-QWP) ·J _(ColLens-HM(T)) ·J _(HM(R)-ColLens) ·J_(pol-HM(R))  (Expression 3)Expression 3 includes no representation of the reference plane mirror 30and the reference spherical mirror 32 since they have negligibleinfluence upon the polarization. J_(pol-M(R)) represents the Jonesmatrix in the optical path from the emergence from the polarizer 11 tothe reflection by the half mirror 14. J_(HM(R)-ColLens) represents theJones matrix in the optical path from the reflection by the half mirror14 to the transmission through the collimator lens 19. J_(Lens)represents the Jones matrix of the test object OS, and J_(ColLens-HM(T))represents the Jones matrix in the optical path from the transmissionthrough the collimator lens 19 to the incidence on the λ/4 plate 27.

The Jones matrix J_(HM(R)-ColLens) in the optical path from thereflection by the half mirror 14 to the transmission through thecollimator lens 19 is equal to the Jones matrix J_(ColLens-HM(T)) in theoptical path from the transmission through the collimator lens 19 to theincident on the λ/4 plate 27. Thus, the following expression 4 holds:J _(HM(R)-ColLens)=(Jsys2⁻¹ ·Jsys3·(Jsys2⁻¹·Jsys1)⁻¹)^(−1/2)  (Expression 4)The Jones matrix J_(Lens) of the test object OS is represented as thefollowing expression 5, and only the Jones matrix J_(Lens) of the testobject OS can be calculated.J _(Lens)=(Jsys2⁻¹(Jsys2⁻¹ ·Jsys3·(Jsys2⁻¹ ·Jsys1)⁻¹)^(−1/2)·Jtest·(Jsys2⁻¹ ·Jsys3·(Jsys2⁻¹ ·Jsys1)⁻¹)⁻²·(Jsys2⁻¹·Jsys1)⁻¹)^(−1/2)  (Expression 5)

In this manner, the measuring apparatus 1 can measure the Jones matrixwhich is the polarization characteristic matrix of the test object OS.To derive the phase lag and the optical characteristic direction whichare birefringence characteristics from the Jones matrix, an eigenvalueand an eigenvector of the Jones matrix J_(Lens) of the test object OSmay be determined to derive a phase lag from a phase difference betweentwo sets of eigenvalues, and a characteristic axial angle from the angleof an eigenvector.

Next, description will be made of normalization of the Jones matrixusing a predetermined (that is, a known) transmitted wavefront tocalculate a wavefront in polarization distribution in the pupil plane ofthe test object OS. First, a transmitted wavefront W_(in)(r, θ) ismeasured in the pupil plane of the test object OS for predeterminedincident polarization, where (r, θ) represents the coordinates on thepupil plane of the test object OS. Embodiment 1 takes an example inwhich linear polarization E_(in)=(1,0) in an X direction is incident.

Next, a transmitted wavefront P_(in)(r, θ) in the pupil plane providedin interference measurement is calculated from the Jones matrixJ_(Lens)(r, θ) in the pupil plane which is the polarizationcharacteristic of the test object OS. When the polarization state E_(in)is incident, luminous flux under test E_(out) (r, θ) is represented asthe following expression 6 by using the Jones matrix in the pupil plane:$\begin{matrix}{{{E_{out}\left( {r,\theta} \right)} = {{{J_{Lens}\left( {r,\theta} \right)}E_{in}} = \begin{pmatrix}{J_{Lens}11\left( {r,\theta} \right)} \\{J_{Lens}21\left( {r,\theta} \right)}\end{pmatrix}}}{{J_{Lens}\left( {r,\theta} \right)} = \begin{pmatrix}{J_{Lens}11\left( {r,\theta} \right)} & {J_{Lens}12\left( {r,\theta} \right)} \\{J_{Lens}21\left( {r,\theta} \right)} & {J_{Lens}22\left( {r,\theta} \right)}\end{pmatrix}}} & \left( {{Expression}\quad 6} \right)\end{matrix}$On the other hand, reference luminous flux in the incident state E_(in)is perpendicularly reflected and returned. Thus, the transmittedwavefront P_(in)(r, θ) on the pupil plane provided in interferencemeasurement for the incident polarization E_(in) is represented as thefollowing expression 7:

=

  (Expression 7)Since the actually measured transmitted wavefront in the pupil plane ofthe test object OS is W_(in)(r, θ), the Jones matrix J_(Lens) 0 providedby normalizing the transmitted wavefront P_(in)(r, θ) for the offset isrepresented as the following expression 8: $\quad\begin{matrix}\begin{matrix}{{J_{Lens}0\left( {r,\theta} \right)} = {{\exp\left( {{2{\pi\mathbb{i}}\quad{W_{in}\left( {r,\theta} \right)}} - {P_{in}\left( {r,\theta} \right)}} \right)}{J_{Lens}\left( {r,\theta} \right)}}} \\{= {\exp\left( {{2{\pi\mathbb{i}}\quad{W_{in}\left( {r,\theta} \right)}} - {\arg\left( {J_{Lens}11\left( {r,\theta} \right)} \right)}} \right)}} \\{J_{Lens}\left( {r,\theta} \right)}\end{matrix} & \left( {{Expression}\quad 8} \right)\end{matrix}$Thus, the wavefront in arbitrary polarization distribution can becalculated from the Jones matrix J_(Lens) 0. Such calculation can bemade for all the pixels in the pupil of the test object OS to calculatethe phase lag and the characteristic axial angle which are birefringencecharacteristics of the test object OS and the wavefront in arbitrarypolarization distribution.

Embodiment 2

FIG. 4 is a schematic section view showing the structure of a measuringapparatus 1A according to an aspect of the present invention. Themeasuring apparatus 1A of Embodiment 2 includes a Fizeau interferometerfor measuring a wavefront (a transmitted wavefront) of light transmittedthrough a test object OS and measures birefringence of the test objectOS. Since the measurement of the Jones matrix of the test object OSassociated with the measurement of the polarization characteristicmatrix is similar to that in Embodiment 1, description will be made onlyof separation of luminous flux under test from reference luminous fluxperformed in a different manner from that in Embodiment 1.

Referring to FIG. 4, luminous flux which emitted from a light source 10is linearly polarized at an arbitrary angle by a λ/2 plate 41 and apolarizer 11. The luminous flux which emerged from the polarizer 11 isonce condensed by a beam expander 12 and is reflected and diverged by ahalf mirror 14. The luminous flux which was reflected by the half mirror14 is collimated by a beam expander 13 to have an increased beamdiameter. The luminous flux which passed through the beam expander 13 isreflected by a mirror 42, enters an object-side XY stage 15, isreflected by an X stage return mirror 16 to a mirror on a Y stage, notshown, and is then reflected by a mirror 17 to an object-side Z stage18.

A so-called TS lens 44 is disposed across a PZT actuator 43 from theobject-side Z stage 18. The TS lens 44 has a radius of curvature of afinal surface equal to the distance from the final surface to the focalpoint. The object-side Z stage 18 is driven such that the convergingposition of the luminous flux transmitted through the TS lens 44 (thefocal point of the TS lens 44) is at the object surface of the testobject OS. The object-side XY stage 15 is driven such that theconverging position of the luminous flux transmitted through the TS lens44 is at the object position where birefringence is measured.

The TS lens 44 has an antireflective coating film except on the finalsurface for the wavelength of light from the light source 10, and onlythe final surface is made of raw glass with no coating. Thus,approximately 5% of the incident light amount is reflected by the finalsurface of the TS lens 44 and returned to the half mirror 14 along thesame optical path. The luminous flux reflected by the final surface ofthe TS lens 44 will hereinafter be referred to as reference luminousflux.

The luminous flux which passed through the TS lens 44 and entered thetest object OS is transmitted through the test object OS and is formedinto an image at an image point determined by the magnification of thetest object OS. A spherical mirror 21 is disposed on an image-side Zstage 20.

In Embodiment 2, when birefringence of the test object OS is measured,the image-side Z stage 20 and an image-side XY stage 22 adjust theposition such that the image-forming position (the image point) of thetest object OS is shifted by Δ from the center of curvature of thespherical mirror 21 in the direction perpendicular to the optical axisof the measuring optical system (the test object OS). On the other hand,in measuring the transmitted wavefront, the spherical mirror 21 isdisposed such that the image-forming position of the test object OScoincides with the center of curvature of the spherical mirror 21. Thespherical mirror 21 is made of raw glass similarly to the final surfaceof the TS lens 44. The luminous flux reflected by the spherical mirror21 will hereinafter be referred to as luminous flux under test.

The reference luminous flux which was reflected by the final surface ofthe TS lens 44 travels along the same optical path and is transmittedthrough the half mirror 14. On the other hand, the luminous flux undertest which was reflected by the spherical mirror 21 travels and isincident on the half mirror 14 along the return path inclined withrespect to the go path since the center of curvature of the sphericalmirror 21 is shifted by Δ from the image-forming position. The shiftamount Δspf between the luminous flux under test and the referenceluminous flux on a spatial filter 45 disposed at the position conjugateto the focal point of the TS lens 44 is represented as the followingexpression 9:

spf=2×

/βLens×Fexp/Fts  (Expression 9)where βLens represents the lateral magnification of the test object OS,Fts the focal length of the TS lens 44, and Fexp the focal length of thebeam expander 13.

The shift amount Δspf shown by expression 9 is used to separate theluminous flux under test from the reference luminous flux. FIGS. 5(a)and 5(b) are enlarged section views showing the spatial filter(aperture) 45 and its surroundings. The spatial filter is disposed atthe position optically conjugate to the object surface and the imageplane of the test object OS. In FIGS. 5(a) and 5(b), dashed lines showthe optical axis of the measuring optical system. As shown in FIG. 5(a),the center of an opening 45 a of the spatial filter 45 is on the opticalaxis of the measuring optical system in normal interferometermeasurement. On the other hand, in measuring birefringence, as shown inFIG. 5(b), the spatial filter 45 is shifted by the amount Δspf to movethe center of the opening 45 a of the spatial filter 45 to the positionwhere the luminous flux under test is converged, thereby blocking thereference luminous flux and transmitting only the luminous flux undertest.

The luminous flux under test which passed through the spatial filter 45is transmitted through a pupil image-forming lens 26 and collimated. Thecollimated luminous flux under test is subjected to polarizationmodulation by a λ/4 plate 27. Then, only the polarization componentthereof in the transmission axis direction of a polarizer 28 isextracted by the polarizer 28, and taken as an image by a camera 29. Thebeam expander 13 and the pupil image-forming lens 26 cause the apertureof the TS lens 44 to be conjugate to the camera 29 and cause theaperture of the TS lens 44 to be conjugate to the pupil of the testobject OS. Thus, the camera 29 is conjugate to the pupil of the testobject OS.

The measuring apparatus 1A described above is used to measure emergencepolarization for a plurality of incident polarization states provided bythe polarizer 11 to derive the Jones matrix which is a polarizationcharacteristic matrix of the luminous flux under test, similarly toEmbodiment 1. Then, the Jones matrix resulting from the measuringoptical system other than the test object OS can be removed to measurethe polarization characteristic matrix in the pupil plane of the testobject OS.

Embodiment 3

Embodiment 3 will be described in conjunction with a method of averaginginterference patterns by using fringe scan, separating luminous fluxunder test from reference luminous flux, and measuring a polarizationcharacteristic matrix of a test object OS. Embodiment 1 employs thelight shield plate 24 to block the reference luminous flux andEmbodiment 2 employs the spatial filter 45 to block the referenceluminous flux, thereby detecting only the luminous flux under test. InEmbodiment 3, however, reference luminous flux is not blocked, and onlythe information about luminous flux under test is taken out byaccumulating the intensity of interference patterns. Description willhereinafter be made mainly of the structure and operation different fromthose in Embodiment 2.

In Embodiment 3, in the structure of the measuring apparatus 1A shown inFIG. 4, the image-side Z stage 20 and the image-side XY stage 22 areadjusted such that the center of curvature of the spherical mirror 21coincides with the image-forming point of the test object OS inmeasuring birefringence of the test object OS. The center of the opening45 a of the spatial filter 45 is disposed on the optical axis of themeasuring optical system. With the arrangement, the camera 29 takesimages of interference patterns from the interference between theluminous flux under test and the reference luminous flux in accordancewith the difference in optical path length between the luminous fluxunder test and the reference luminous flux and the wavefront aberrationof the test object OS.

In measuring the polarization of luminous flux incident on the λ/4 plate27, the PZT actuator 43 displaced on the object-side Z stage 17 islinearly driven by an integral multiple of one-half wavelength for eachof small angle steps of the λ/4 plate 27, and the accumulated lightamount during that period is used to calculate the information about theluminous flux under test.

FIGS. 6(a) and 6(b) are graphs showing the driving of the PZT actuator43 and variations in interference patterns in a pixel of the camera 29.Each time the driving amount of the PZT actuator 43 shown in FIG. 6(b)reaches an integral multiple of one-half wavelength, the intensity ofinterference patterns shown in FIG. 6(a) periodically varies. Theintensity Ifrg of interference patterns is represented as the followingexpression 10:Ifrg=Itest+Iref+2V√{square root over (ItestIref)}cos(2πL/λ)  (Expression10)where Iref represents the light amount of the luminous flux under test,Itest the light amount of the reference luminous flux, V the contrastbetween the interference patterns of the luminous flux under test andthe reference luminous flux, and L the difference in the optical pathlength between the luminous flux under test and the reference luminousflux.

Thus, the accumulated light amount provided when the optical path lengthdifference is changed by the integral multiple of the wavelength isequal to the sum of the amount of the luminous flux under test and theamount of the reference luminous flux, and the interference componentsare canceled out.

In Embodiment 3, the PZT actuator 43 is driven to perform scanning forthe interference patterns. When the wavelength of the light source 10can be changed, the scanning for interference patterns may be performedby changing the wavelength. In such a case, the wavelength changerepresented by the following expression 11 can be used to determinevariations in interference patterns for one cycle:dλ=λ ² /L  (Expression 11)

With the abovementioned measurement, the DC component, the secondharmonic component, and the fourth harmonic component provided when theλ/4 plate 27 is rotated are calculated as the sum of the referenceluminous flux and the luminous flux under test. Only the components ofthe luminous flux under test modulated by the λ/4 plate 27 can becalculated with the following expression 12:DCtest=DCref+test−DCrefSHtest=SHref+test−SHrefFHtest=FHref+test−FHref  (Expression 12)where DCref+test represents the DC component, SHref+test the secondharmonic component, and FHref+test the fourth harmonic component.

Next, the emergence polarization state is calculated from thesemodulated components, and the emergence polarization of the luminousflux under test is measured for a plurality of incident polarizationstates provided by the polarizer 11 to determine the Jones matrix whichis the polarization characteristic matrix of the luminous flux undertest. Then, the Jones matrix resulting from the measuring optical systemother than the test object OS can be removed to determine thepolarization characteristic matrix in the pupil plane of the test objectOS.

Embodiment 4

Embodiment 4 will be described in conjunction with a method of measuringtransmittance distribution in the pupil plane of the test object OS byusing a measuring apparatus having the same structure as that ofEmbodiment 1. In the measurement of the measuring apparatus 1 shown inFIGS. 1A and 3, the Jones matrixes represented by the followingexpression 13 are measured from the system errors 1 and 2:Jtest=J _(HM(T)-QWP) ·J _(ColLens-HM(T)) ·J _(Lens) ·J _(Lens) ·J_(HM(R)-ColLens) ·J _(pol-HM(R))Jsys3=J _(HM(T)-QWP) ·J _(ColLens-HM(T)) ·J _(HM(R)-ColLens) ·J_(pol-HM(R))  (Expression 13)

As described in Embodiment 1, since the Jones matrix calculated from themeasurement of the normal polarization characteristic matrix isnormalized for the elements of two rows and two columns, these arenormalized for the transmittance for entering unpolarized luminous fluxin this case. The transmittance Tup for the unpolarized luminous flux isrepresented by the following expression 14 with each element of theJones matrix J: $\begin{matrix}{{Tup} = {\frac{1}{2}{\sum\limits_{i,j}{J_{ij}}^{2}}}} & \left( {{Expression}\quad 14} \right)\end{matrix}$

Thus, the transmittance may be calculated from the Jones matrixdetermined in Embodiment 1, and each element may be divided by √2Tup.The following expression 15 holds:T _(test) j _(test) =T _(HM(T)-QWP) T _(Lens) ² T _(HM(R)-ColLens) ² T_(pol-HM(R)) j _(HM(T)-QWP) ·j _(ColLens-HM(T)) ·j _(Lens) ·j _(Lens) ·j_(HM(R)-ColLens) ·j _(pol-HM(R))T _(sys3) j _(sys3) =T _(HM(T)-QWP) T _(HM(R)-ColLens) ² T _(pol-HM(R))j _(HM(T)-QWP) ·j _(ColLens-HM(T)) ·j _(HM(R)-ColLens) ·j_(pol-HM(R))  (Expression 15)where j represents the Jones matrix normalized for the unpolarizedluminous flux and T represents the actual transmittance of the opticalelement represented by each Jones matrix for unpolarized luminous flux.

In addition, the following expression 16 holds: $\begin{matrix}{{{I_{test}\left( \chi_{test} \right)} = {T_{test}^{2}{{j_{test} \cdot \begin{bmatrix}1 \\\chi_{test}\end{bmatrix}}}^{2}}}{{I_{{sys}\quad 3}\left( \chi_{{sys}\quad 3} \right)} = {T_{{sys}\quad 3}^{2}{{j_{{sys}\quad 3} \cdot \begin{bmatrix}1 \\\chi_{{sys}\quad 3}\end{bmatrix}}}^{2}}}} & \left( {{Expression}\quad 16} \right)\end{matrix}$where Itest and Isys3 represent the actual light amounts detected by thecamera 29 in the entering polarization Xtest and Xsys3 in measuring theJones matrixes Jtest and Jsys3.

Thus, the transmittance T_(lens) of the test object OS for theunpolarized luminous flux may be calculated from the followingexpression 17: $\begin{matrix}{T_{lens} = \sqrt{\frac{\begin{matrix}{{I_{\quad{test}}\left( \chi_{\quad{test}} \right)}{\quad{j_{\quad{{{HM}{(T)}} - {QWP}}} \cdot \quad j_{\quad{{ColLens} - {{HM}{(T)}}}} \cdot}\quad}} \\{{j_{\quad{{{HM}\quad{(R)}} - {ColLens}}} \cdot \quad j_{\quad{{pol}\quad - \quad{{HM}\quad{(R)}}}}}}^{2}\end{matrix}}{\begin{matrix}{{I_{{sys}\quad 3}\left( \chi_{{sys}\quad 3} \right)}{{j_{\quad{{{HM}{(T)}}\quad - \quad{QWP}}} \cdot j_{\quad{{ColLens}\quad - \quad{{HM}{(T)}}}} \cdot}}} \\{{j_{Lens} \cdot j_{Lens} \cdot j_{\quad{{{HM}\quad{(R)}} - {ColLens}}} \cdot j_{\quad{{pol} - {{HM}\quad{(R)}}}}}}^{2}\end{matrix}}}} & \left( {{Expression}\quad 17} \right)\end{matrix}$

The transmittance for arbitrary polarization may be calculated from thefollowing expression 18: $\begin{matrix}{{{Tlens}\left( \chi_{in} \right)} = {{Tlens}\frac{{{j_{{lens}\quad 11} + {j_{{lens}\quad 12}\chi_{in}}}}^{2} + {{j_{{lens}\quad 21} + {j_{{lens}\quad 22}\chi_{in}}}}^{2}}{1 + {\chi_{in}}^{2}}}} & \left( {{Expression}\quad 18} \right)\end{matrix}$where Xin represents the incident polarization parameter.

Embodiment 5

While Embodiments 1 to 4 include the interferometer having theadditional function of measuring the birefringence (the polarizationcharacteristic matrix), the function of the interferometer may not beprovided. In such a case, the influence of the birefringence of theoptical system other than the test object OS can be removed as describedabove to measure the polarization characteristic matrix in the samestate as that of the interferometer shown in Embodiments 1 to 4.

FIG. 7 shows a schematic section view showing the structure of ameasuring apparatus 1B according to an aspect of the present invention.The measuring apparatus 1B has only the function of measuring apolarization characteristic matrix of a test object OS.

Referring to FIG. 7, luminous flux which emitted from a light source 10is transmitted through a polarizer 11 to have a predetermined (that is,a known) polarization state. The luminous flux emitting from the lightsource 10 is circularly polarized. Simply rotating the polarizer 11 canprovide a sufficient amount of arbitrarily linearly polarized light. Thepolarizer 11 is disposed to be driven on a θ stage, not shown, andcontrolled by a controller, not shown.

The luminous flux which passed through the polarizer 11 is linearlypolarized depending on the angle of the polarizer 11. The luminous fluxwhich passed through the polarizer 11 is transmitted through beamexpanders 12 and 13 for increasing the beam diameter and is incident ona half mirror 14 as collimated luminous flux. Embodiment 4 does not havethe function of an interferometer, so that the measuring apparatus 1Bhas no reference mirror. Thus, the luminous flux which passed throughthe half mirror 14 is blocked by a light shield plate 24. The luminousflux reflected by the half mirror 14 will hereinafter be referred to asluminous flux under test.

The luminous flux under test enters an object-side XY stage 15 and isreflected by an X stage return mirror 16 to a mirror on a Y stage, notshown, and is then reflected by a mirror 17 to an object-side Z stage18. The return by the mirror is performed for the purpose of providingthe same optical axis with respect to the stage even when the stage ismoved, so that the luminous flux may be incident on the mirrors in adifferent order from that in Embodiment 5. A collimator lens 19 isdisposed on the object-side Z stage 18. The object-side Z stage 18 isdriven such that the focal point of the collimator lens 19 is at theobject surface of the test object OS. The object-side XY stage 15 isdriven to the object position where birefringence is measured.

The luminous flux under test which passed through the collimator lens 19and entered the test object OS passes through the test object OS and isformed into an image at an image point which is determined by themagnification of the test object OS. A spherical mirror 21 is disposedon an image-side Z stage 20. The image-side Z stage 20 and an image-sideXY stage 22 adjust the position such that the center of curvature of thespherical mirror 21 coincides with the image-forming position (the imagepoint) of the test object OS.

The luminous flux under test which was reflected by the spherical mirror21 passes through the test object OS and is returned to the half mirror14 along the same optical path. The luminous flux under test whichpassed through the half mirror 14 is transmitted through pupilimage-forming lenses 25 and 26 for providing a conjugate relationshipbetween the pupil of the test object OS and a camera 29, and becomescollimated again. The collimated luminous flux under test is subjectedto polarization modulation by λ/4 plate 27 disposed on a θ stage, notshown. Only the linearly polarized component specified by the angle ofan analyzer 28 is transmitted through the analyzer 28 and is taken as animage by the camera 29. The θstage, not shown, is controlled by acontroller, not shown. The angle of the fast axis of the λ/4 plate 27 atthe origin point of the θstage and the angle of the transmission axis ofthe analyzer 28 are adjusted in parallel with the sheet (FIG. 7),similarly to the transmission axis of the analyzer 28.

A reference plane mirror 30, a polarizer 31, and a reference sphericalmirror 32 can be inserted into and removed from the optical path of theluminous flux under test, as in the measuring apparatus 1.

With the measuring apparatus 1B described above, emergence polarizationis measured for a plurality of incident polarization states provided bythe polarizer 11 to determine the Jones matrix which is the polarizationcharacteristic matrix of the luminous flux under test, similarly toEmbodiment 1. Then, the Jones matrix resulting from the measuringoptical system other than the test object OS can be removed to measurethe polarization characteristic matrix in the pupil plane of the testobject OS.

As described above, according to the measuring apparatus of the presentinvention, errors caused by the system are accurately corrected withoutconsidering the state of the test object (such as the direction of thefast axis of the test object) although the interferometer is used. Thisallows precise measurement of the polarization characteristic matrixwhich is the polarization characteristic in the pupil plane of the testobject. The birefringence distribution and the transmittancedistribution in the pupil plane of the test object can also be measuredaccurately from the measured polarization characteristic matrix. Inaddition, the polarization characteristic matrix can be measured in thesame state as that in measurement with the interferometer, so that thewavefront in the pupil plane of the test object in arbitrarypolarization distribution can be measured precisely.

While the preferred embodiments of the present invention have beendescribed, it goes without saying that the present invention is notlimited to the abovementioned embodiments, and various modifications andvariations may be made without departing from the spirit and scopethereof. For example, it is obvious that a catadioptric system formed ofa lens and a mirror or a reflective system formed of a mirror may beused as the test object OS in each of Embodiments 1 to 5 in addition tothe refractive optical system formed only of the lenses. In addition,the interferometer of Embodiments 1 to 5 may be installed on an exposureapparatus. (see U.S. Pat. No. 6,614,535B1)

This application claims a foreign priority benefit based on JapanesePatent Application No. 2005-027498 filed on Feb. 3, 2005, which ishereby incorporated by reference herein in its entirety as if fully setforth herein.

1-14. (canceled)
 15. A measuring apparatus configured to measure apolarization characteristic and a transmission wavefront of a testobject, said measuring apparatus comprising: a beam splitter configuredto split light from a light source into reference light and light undertest; and a detector configured to detect the reference light and thelight under test, wherein the transmission wavefront of the test objectis measured when the detector detects an interference pattern formed byinterference between the light under test and the reference light, and apolarization characteristic matrix in a pupil plane of the test objectis measured when a light shielding member shields the reference lightand the detector detects only the light under test.
 16. The measuringapparatus according to claim 15, wherein the light shielding memberincludes a light shield plate which can be inserted into and removedfrom an optical path between the beam splitter and the detector, andwherein the reference light is blocked by the light shield plate placedin the optical path.
 17. The measuring apparatus according to claim 15,comprising a spherical mirror which reflects the light under test whichhas passed the test object and directs the reflected light again to thetest object, wherein the light shielding member includes the spatialfilter which is disposed on a plane where the reference light isconverged, and wherein the reference light is blocked by the spatialfilter when the spherical mirror and the spatial filter are moved. 18.The measuring apparatus according to claim 15, wherein the measuringunit includes: a wavelength plate configured to provide a predeterminedphase lag to the light under test; and a polarizer configured to extractonly a linearly polarized light component in an arbitrary direction fromthe light under test that has passed through the wavelength plate. 19.The measuring apparatus according to claim 18, wherein the wavelengthplate is a λ/4 plate.
 20. The measuring apparatus according to claim 18,wherein the polarizer is a Rochon prism.
 21. The measuring apparatusaccording to claim 15, further comprising a normal-incidence reflectivemirror which can be inserted into and removed from an optical path ofthe light under test.
 22. The measuring apparatus according to claim 15,wherein the polarization characteristic matrix is the Jones matrix.